7.8.1 dim (letterplace)

Syntax:

dim( ideal_expression)

Type:

int

Purpose:

Compute the Gelfand-Kirillov dimension of the algebra basering/(input ideal). Uses Ufnarovskij graph for computations.

Note:

the input ideal must be given as a two-sided Groebner basis.

Example:

LIB "freegb.lib"; ring r = 0,(x,y,z),dp; ring R = freeAlgebra(r, 5); ideal I = z; dim(twostd(I)); // GK dimension is infinite ==> -1 I = x,y,z; dim(twostd(I)); ==> 0 I = x*y, x*z, z*y, z*z; dim(twostd(I)); ==> 2 I = y*x - x*y, z*x - x*z, z*y - y*z; I = twostd(I); I; ==> I[1]=z*y-y*z ==> I[2]=z*x-x*z ==> I[3]=y*x-x*y dim(I); // 3, as expected for R/I = K[x,y,z] ==> 3